// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Desire NUENTSA WAKAM <desire.nuentsa_wakam@inria.fr
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_ITERSCALING_H
#define EIGEN_ITERSCALING_H

namespace Eigen {

/**
  * \ingroup IterativeSolvers_Module
  * \brief iterative scaling algorithm to equilibrate rows and column norms in matrices
  * 
  * This class can be used as a preprocessing tool to accelerate the convergence of iterative methods 
  * 
  * This feature is  useful to limit the pivoting amount during LU/ILU factorization
  * The  scaling strategy as presented here preserves the symmetry of the problem
  * NOTE It is assumed that the matrix does not have empty row or column, 
  * 
  * Example with key steps 
  * \code
  * VectorXd x(n), b(n);
  * SparseMatrix<double> A;
  * // fill A and b;
  * IterScaling<SparseMatrix<double> > scal; 
  * // Compute the left and right scaling vectors. The matrix is equilibrated at output
  * scal.computeRef(A); 
  * // Scale the right hand side
  * b = scal.LeftScaling().cwiseProduct(b); 
  * // Now, solve the equilibrated linear system with any available solver
  * 
  * // Scale back the computed solution
  * x = scal.RightScaling().cwiseProduct(x); 
  * \endcode
  * 
  * \tparam _MatrixType the type of the matrix. It should be a real square sparsematrix
  * 
  * References : D. Ruiz and B. Ucar, A Symmetry Preserving Algorithm for Matrix Scaling, INRIA Research report RR-7552
  * 
  * \sa \ref IncompleteLUT 
  */
template <typename _MatrixType> class IterScaling
{
public:
    typedef _MatrixType MatrixType;
    typedef typename MatrixType::Scalar Scalar;
    typedef typename MatrixType::Index Index;

public:
    IterScaling() { init(); }

    IterScaling(const MatrixType& matrix)
    {
        init();
        compute(matrix);
    }

    ~IterScaling() {}

    /** 
     * Compute the left and right diagonal matrices to scale the input matrix @p mat
     * 
     * FIXME This algorithm will be modified such that the diagonal elements are permuted on the diagonal. 
     * 
     * \sa LeftScaling() RightScaling()
     */
    void compute(const MatrixType& mat)
    {
        using std::abs;
        int m = mat.rows();
        int n = mat.cols();
        eigen_assert((m > 0 && m == n) && "Please give a non - empty matrix");
        m_left.resize(m);
        m_right.resize(n);
        m_left.setOnes();
        m_right.setOnes();
        m_matrix = mat;
        VectorXd Dr, Dc, DrRes, DcRes;  // Temporary Left and right scaling vectors
        Dr.resize(m);
        Dc.resize(n);
        DrRes.resize(m);
        DcRes.resize(n);
        double EpsRow = 1.0, EpsCol = 1.0;
        int its = 0;
        do
        {  // Iterate until the infinite norm of each row and column is approximately 1
            // Get the maximum value in each row and column
            Dr.setZero();
            Dc.setZero();
            for (int k = 0; k < m_matrix.outerSize(); ++k)
            {
                for (typename MatrixType::InnerIterator it(m_matrix, k); it; ++it)
                {
                    if (Dr(it.row()) < abs(it.value()))
                        Dr(it.row()) = abs(it.value());

                    if (Dc(it.col()) < abs(it.value()))
                        Dc(it.col()) = abs(it.value());
                }
            }
            for (int i = 0; i < m; ++i) { Dr(i) = std::sqrt(Dr(i)); }
            for (int i = 0; i < n; ++i) { Dc(i) = std::sqrt(Dc(i)); }
            // Save the scaling factors
            for (int i = 0; i < m; ++i) { m_left(i) /= Dr(i); }
            for (int i = 0; i < n; ++i) { m_right(i) /= Dc(i); }
            // Scale the rows and the columns of the matrix
            DrRes.setZero();
            DcRes.setZero();
            for (int k = 0; k < m_matrix.outerSize(); ++k)
            {
                for (typename MatrixType::InnerIterator it(m_matrix, k); it; ++it)
                {
                    it.valueRef() = it.value() / (Dr(it.row()) * Dc(it.col()));
                    // Accumulate the norms of the row and column vectors
                    if (DrRes(it.row()) < abs(it.value()))
                        DrRes(it.row()) = abs(it.value());

                    if (DcRes(it.col()) < abs(it.value()))
                        DcRes(it.col()) = abs(it.value());
                }
            }
            DrRes.array() = (1 - DrRes.array()).abs();
            EpsRow = DrRes.maxCoeff();
            DcRes.array() = (1 - DcRes.array()).abs();
            EpsCol = DcRes.maxCoeff();
            its++;
        } while ((EpsRow > m_tol || EpsCol > m_tol) && (its < m_maxits));
        m_isInitialized = true;
    }
    /** Compute the left and right vectors to scale the vectors
     * the input matrix is scaled with the computed vectors at output
     * 
     * \sa compute()
     */
    void computeRef(MatrixType& mat)
    {
        compute(mat);
        mat = m_matrix;
    }
    /** Get the vector to scale the rows of the matrix 
     */
    VectorXd& LeftScaling() { return m_left; }

    /** Get the vector to scale the columns of the matrix 
     */
    VectorXd& RightScaling() { return m_right; }

    /** Set the tolerance for the convergence of the iterative scaling algorithm
     */
    void setTolerance(double tol) { m_tol = tol; }

protected:
    void init()
    {
        m_tol = 1e-10;
        m_maxits = 5;
        m_isInitialized = false;
    }

    MatrixType m_matrix;
    mutable ComputationInfo m_info;
    bool m_isInitialized;
    VectorXd m_left;   // Left scaling vector
    VectorXd m_right;  // m_right scaling vector
    double m_tol;
    int m_maxits;  // Maximum number of iterations allowed
};
}  // namespace Eigen
#endif
